A deal was struck with RB Leipzig during the summer which will see him become a Liverpool player come July 1.
The 22-year-old is due to see out the current campaign with the Bundesliga outfit.
But hopes have been raised of late among Reds supporters that Keita could make the switch earlier than planned.
Leipzig have struggled in their Champions League debut so far, making progression to the knockout stages a tough ask.
As a result, it was felt Liverpool could look into bring Keita to Anfield in the New Year.
However, according to the Liverpool Echo, that prospect is unlikely due to two factors.
It is said there is no such agreement in place between the two clubs regarding an early move.
Bringing the centre-midfielder to Merseyside in January would also come at a considerable extra cost to Liverpool.
Reports have claimed should Jurgen Klopp secure Keita's arrival in January, it may facilitate Emre Can's transfer to Juventus.
The Germany international is yet to agree a new contract with the Reds, and Keita has added to the uncertainty over Can's future.
But it appears Keita is expected to be staying put at Leipzig until next summer.
Leipzig sit fourth in the Bundesliga table after seven games, although Keita has endured a tough spell with disincline of late.
His manager, Ralph Hasenhuttl, feels the Guinea star is now a marked man and said: "We need to be careful not to stigmatise him. He’s obviously now a player who others try to provoke, but he has learned his lesson.”
Liverpool would love to Keita in their ranks this Saturday as they prepare to take on Manchester United at Anfield (12.30pm).
